Poisson Processes: Examples

This lecture delves into Poisson processes, starting with a question on exponential random variables and their relevance to Poisson processes. The instructor provides three proofs showing that a random variable T is exponential beta lambda. The lecture then explores scenarios involving customer arrivals in a store following a Poisson-Lander process, discussing the probabilities of specific events such as the number of customers arriving, making purchases, and the store closing at a certain time. The concept of Poisson processes is further illustrated through examples and calculations, demonstrating the application of Poisson distributions in real-world scenarios.